Tag Archives: mastery

At the start of this academic year I wanted to really put the theory of learning I knew into practice. Here are three teaching techniques I tried that I’ll be taking with me into 2015.

1. Interleave *everything*
We know that interleaving concepts and procedures is a desirable difficulty that improves learning. This year I’ve made it my aim to never teach a lesson that uses only one topic. Extension work doesn’t count: the main bulk of a lesson must include multiple concepts. In practice, this means that every set of questions I write includes applying the new thing being learned to problems involving other concepts from earlier on in the curriculum. I found this daunting at first – “what if it’s just too confusing for them?” – but I’ve found there’s tremendous power in my expectation that they can competently use everything I have taught them, at any time.

It’s also made the questions I write far richer and more interesting than ever before. A standard lesson on volume would include questions on upper and lower bounds, percentage changes to a volume when dimensions change by different percentages, and using Pythagoras’ Theorem to find missing dimensions before calculating a volume. These questions were the normal ones. They were not special extension questions for the top 20%. The message this broadcast, combined with the cognitive effect of the desirable difficulty, has made a noticeable impact on learning.

2. Spaced testing of *everything*
We know that spacing and testing are two of the most powerful tools in an educators’ arsenal. So I’ve made it my aim to space out testing of everything my students’ have studied.

The first way I’ve done this is through our departmental testing. This year we’re using low-stakes quizzes on each topic as a replacement for the half-termly summative tests we used to use. What’s great about this is that each topic has two quizzes: one taken at the end of the topic, and one a month later. This reinforces the expectation that students should remember what they’ve been taught, and incentivises them to revisit their learning when it will have the biggest impact on longer-term retention.

The second way is through an idea I’ve borrowed from Bruno Reddy and Kris Boulton at KSA. Long ago they told me about “Only 100% Will Do” starters: simple recall or procedural questions that had been previously studied. Now my students begin every lesson with an “Only 100% Will Do” sheet where they work on concepts from any past year group to make sure that they’re keeping up to speed.

3.Lightning fast in-class assessment
I have always been a big fan of in-class assessment, and could singlehandedly prop up the UK’s mini-whiteboard industry. But over the summer Joe Kirby introduced me to an app called Quick Key. It changed my life!

Quick Key is an optical scanning app for mobile phones. It works by scanning in students’ answer sheets to a multiple choice quiz, and giving you great analytics on your phone or in a spreadsheet. It’s also fast – I can scan a whole class set of answers in about a minute. This lets me pinpoint exactly how well the class are doing at a topic. I will discover that one mistake or misconception is bogging down the whole room, or that four students need extra support in this lesson and another five need extra challenge. The laser-like precision with which I can adapt during a lesson or plan the next one is having a big impact on my teaching.

Like any technique, these three have worked well because I made them a habit. We do these three things in the same way in almost every lesson. This consistency no doubt aids their effectiveness. But they are nonetheless three real techniques that put into practice the theory of learning we know to be so powerful.

Mastery learning is the belief that students should master a skill before moving on to learn a new one. In contrast to the classic spiral curriculum, where students raced between topics without properly learning any of them, a mastery curriculum gives students the space to learn a skill, understand it conceptually, and practise until it’s automatic.

This approach matters because of its effect on working memory. Students who have mastered previous skills have their working memory freed to learn new ones, while students who haven’t get bogged down in the basics and don’t have the working memory space to learn something new.

There are some important subtleties of definition that Steve Chinn picks up on. What it means to have mastered a topic must be clearly defined from the outset, or confusion will ensue. As understanding improves when students develop their conceptual map of maths and draw links between topics, we know that mastery early in school will not mean perfection. For me, mastery means two things:

The student can demonstrate or explain the concept orally, concretely, visually and abstractly.

The student can apply the concept automatically, so that it is not dominating their working memory.

Chinn does not engage with these fundamentals of mastery learning.

His first criticism is that mastery learning will not help children catch up, and that they should instead be taught with an emphasis “on understanding maths concepts”. Given that Singapore Maths and its mastery model is renowned for its focus on developing understanding, this seems like an odd criticism. Conceptual understanding is at the heart of mastery learning, especially of Singapore Maths and its concrete-pictorial-abstract model of learning mathematical concepts.

His second criticism is that mastery learning is flawed because the ordering of skills for teaching is imperfect. This is true – there is no universally accepted hierarchy of all skills. This does not detract from the obvious fact that some skills are dependent on others, and that these dependencies are important for the order in which we teach. Adding fractions requires a knowledge of lowest common multiples, which requires a knowledge of times tables. We may disagree on whether we should teach names of shapes or bar charts first in the gap between them, but we know they have to come in that order.

The next criticism is that mastery learning is flawed because some people, for unknown reasons, appear to learn things differently. Even if we accept this argument, I cannot see where it leads. Is the implication that we therefore don’t need to care about the order in which we teach topics, and should pull them from a hat? If order doesn’t matter for some people, why deprive the others of being taught in a logical sequence?

It is particularly dangerous to support such arguments with anecdotal success stories like the dyslexic maths student whose times table recall was not perfect. Anecdotes do not a policy make. This anecdote seems compelling precisely because it is so rare, and it is so rare because it is an exception to a large body of well established research. This student succeeded in spite of imperfect times tables, not because of them. That they succeeded against the odds is not a reason for us to stack the odds against everybody else.